The couple, who married in 1981 and have two children together, announced that they are separating but “remain good friends”.
In a statement provided to HuffPost UK, Björn and Lena Ulvaeus said: “After many wonderful and eventful years, we have decided to go our separate ways.
“We remain close friends and will continue to celebrate our grandchildren’s birthdays and other family holidays together.”
The couple met at a New Year’s party at the home of Björn’s ABBA bandmates Benny Andersson and Anni-Frid Lyngstad.
“We really fell in love with lightning,” Björn previously said about Lena.
“So strange that you are a bachelor for a week and then just fall there right away.”
The 75-year-old had previously been married to ABBA’s Agnetha Fältskog between 1971 and 1979.
ABBA formed in Stockholm in 1972 before winning the Eurovision Song Contest in 1974 with their song Waterloo.
They went on to enjoy huge global fame thanks to hits including Dancing Queen, Super Trouper, Voulez Vous and The Winner Takes it All.
In 1999 a musical, Mamma Mia!, hit the stage with a plot based around their hit songs.